Lévy processes have been widely used to model a large variety of stochastic processes under anomalous diffusion. In this note we show that Lévy processes play an important role in the study of the Generalized Langevin Equation (GLE). The solution to the GLE is proposed using stochastic...

Porous materials such as sedimentary rocks often show a fractal character at certain length scales. Deterministic fractal generators, iterated upto several stages and then repeated periodically, provide a realistic model for such systems. On the fractal, diffusion is anomalous, and obeys the law...

We investigate the solutions of a generalized diffusion equation which extends some known equations such as the fractional diffusion equation and the porous medium equation. We start our study by considering the linear case and the nonlinear case afterward. The linear case is analyzed taking...

In this paper we investigate asymptotic behavior of the tail probability for subordinated self-similar processes with regularly varying tail probability. We show that the tail probability of the one-dimensional distributions and the supremum tail probability are regularly varying with the...

We study the resonances of the quantum kicked rotor subjected to an excitation that follows a deterministic time-dependent prescription. For the primary resonances we find an analytical relation between the long-time behavior of the standard deviation and the external kick strength. For the...

We report on decay problem of classical systems. Mesoscopic level consideration is given on the basis of transient dynamics of non-interacting classical particles bounded in billiards. Three distinct decay channels are distinguished through the long-tailed memory effects revealed by temporal...

The paper presents the random-variable formalism of the anomalous diffusion processes. The emphasis is on a rigorous presentation of asymptotic behaviour of random walk processes with infinite mean random time intervals between jumps. We elucidate the role of the so-called inverse-time...

We investigate an N-dimensional fractional diffusion equation with radial symmetry by taking a spatial and time dependent diffusion coefficient into account, i.e., D˜(r,t)=D(t)r−η with D(t)=Dδ(t)+D¯(t). The equation is considered in a confined region and subjected to time dependent...

The relaxation functions for a given generalized Langevin equation in the presence of a three parameter Mittag-Leffler noise are studied analytically. The results are represented by three parameter Mittag-Leffler functions. Exact results for the velocity and displacement correlation functions of...

We investigate the solutions of a fractional diffusion equation with radial symmetry by using the Green function approach and by taking the N-dimensional case into account. In our analysis, a spatial time-dependent diffusion coefficient is considered, i.e., D(r,t)=Dtδ-1r-θ/Γ(α). The presence...